feat(backend): add dependency injection and update main entry point

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

backend/app/core/dependencies.py

@@ -0,0 +1,24 @@
+from __future__ import annotations
+
+from functools import lru_cache
+
+from app.core.config import Settings, get_settings
+
+@lru_cache()
+def get_settings_cached() -> Settings:
+    return get_settings()
+
+
+# Placeholder for future DI wiring. Tests patch classes directly, so we keep
+# a minimal API here to avoid import-time side effects.
+def get_llm_client():
+    settings = get_settings_cached()
+    from app.services.llm_client import LLMClient
+    return LLMClient(settings)
+
+
+def get_rag_service():
+    # Import lazily to avoid circular imports in tests
+    from app.services.rag import RAGService
+    llm = get_llm_client()
+    return RAGService(llm_client=llm)

backend/app/main.py

@@ -2,12 +2,14 @@ from fastapi import FastAPI
 from fastapi.middleware.cors import CORSMiddleware
 
 from app.routers import ingest, query
+from app.core.config import get_settings
 
+settings = get_settings()
 app = FastAPI(title="RAG Video Q&A", version="1.0.0")
 
 app.add_middleware(
     CORSMiddleware,
-    allow_origins=["http://localhost:5173", "http://localhost:3000"],
+    allow_origins=settings.cors_origins,
     allow_credentials=True,
     allow_methods=["*"],
     allow_headers=["*"],